Syllabus

Harvard College/GSAS: 8434,, Exam Group 1, Spring 2012
Instructor: Oliver Knill

Meeting time: Monday/Wednesday/Friday at 10 in 309, and a weekly problem section to be arranged.

The development of calculus by Newton and Leibniz ranks among the greatest intellectual achievements of the past millennium. This course will help you see why. How does differential calculus treat rates of change? How does integral calculus deal with accumulation? And how does the fundamental theorem of calculus link the two? These ideas will be applied to problems from many other disciplines. We do not go chronologically through the textbook but use a slightly streamlined path which will allow us to spend the last week with applying the material. The handouts will guide you.

Course assistants: Jeanine Sinanan-Singh (jsinanan-singh.harvard.edu) Jared Sawyer (jaredsawyer.harvard.edu) Gen Ed: This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.

Prerequisite: A solid background in precalculus.

MQC the MQC for 1A is in SC 309-A from Sun to Thu 8:30 - 10:30 PM. Calendar: the midterm dates are March 1 and April 5, both midterms take place at 6-7:30 PM in Hall E.
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So Mo Tu We Th Fr Sa
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22 23 24 25 26 27 28    4  Jan 23, first class
29 30 31  1  2  3  4    5  Feb
 5  6  7  8  9 10 11    6
12 13 14 15 16 17 18    7
19 20 21 22 23 24 25    8  Feb 20 Presidents day
26 27 28 29  1  2  3    9  Mar 1 First midterm Hall E 6PM
 4  5  6  7  8  9 10   10
11 12 13 14 15 16 17   11
18 19 20 21 22 23 24   12
25 26 27 28 29 30 31   13 
 1  2  3  4  5  6  7   14  Apr 5 Second midterm Hall E 6PM
 8  9 10 11 12 13 14   15
15 16 17 18 19 20 21   16
22 23 24 25 26 27 28   17
29 30  1  2  3  4  5   18  April 26-May 3 Reading period
 6  7  8  9 10 11 12   19  May 4 - May 12 Exam period
13 14 15 16 17 18 19   20
20 21 22 23 24 25 26   21
27 28 29 30 31         22
1. What is calculus?                         Date   Day  
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1. What is Calculus?                         Jan 23 Mon   
2. Functions                                 Jan 25 Wed   
3. Limits                                    Jan 27 Fri   

4  Continuity                                Jan 30 Mon   
5  Intermediate value theorem                Feb  1 Wed   
6. A fundamental theorem                     Feb  3 Fri  

7. Rate of Change, tangent                   Feb  6 Mon   
8. Derivative as a function                  Feb  8 Wed   
9. Product and Quotient rules                Feb 10 Fri   

2. The derivative
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1. Chain rule                                Feb 13 Mon   
2. Critical points and extrema               Feb 15 Wed   
3. Optimization problems                     Feb 17 Fri   

   Pesidents day, no class                   Feb 20 Mon  

4. L'Hopital rule                            Feb 22 Wed   
5. Newton method                             Feb 24 Fri   

6  Review for first midterm  3/1/11          Feb 27 Mon  
7. Rolles theorem                            Feb 29 Wed 
8. Castastrophe theory                       Mar  2 Fri  

3. The integral
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1. From sums to integrals                    Mar  6 Mon  
2. The fundamental theorem                   Mar  8 Wed   
3. Antiderivatives                           Mar 10 Fri  

4. Computing areas                           Mar 19 Mon 
5. Volume of solids                          Mar 21 Wed 
6. Improper integrals                        Mar 23 Fri 

7. Applications of integration               Mar 26 Mon 

4. Calculus Techniques
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1. Related rates                             Mar 28 Wed 
2. Implicit differentiation                  Mar 30 Fri 

3. Substitution                              Apr  2 Wed  
4  Review for second midterm 4/5/11          Apr  4 Mon   
5. Integration by parts                      Apr  6 Fri  

6. Numerical integration                     Apr  9 Mon  
7. Partial fractions                         Apr 11 Wed  
8. Trig substitutions                        Apr 13 Fri  

5. Calculus and the world
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1. Calculus and music                        Apr 16 Mon  
2. Calculus and statistics                   Apr 18 Wed  
3. Calculus and economics                    Apr 20 Fri  

1. Calculus and Computing                    Apr 23 Mon  
2. Outlook and review                        Apr 25 Mon